Question

please help me to solve this question​

Answer 1

Answer:

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Answer 2

${\huge{\red{\mathtt{Hey\:Mate!!}}}}$

${\bold{\underline{Here\:is\:the\:answer}}}$→

$= > \frac{sin \: ( \theta + \alpha ) + cos \: ( \theta - \alpha )}{sin \: ( \theta - \alpha) + cos( \theta + \alpha )} \\ \\ = > \frac{sin \theta.cos \alpha + cos \theta.sin \alpha + cos \theta.cos \alpha + sin \theta.sin \alpha }{{sin \theta.cos \alpha - cos \theta.sin \alpha + cos \theta.cos \alpha - sin \theta.sin \alpha } } \\ \\ = > \frac{sin \alpha(cos \theta + sin \theta) + cos \alpha (cos \theta + sin \theta) }{{sin \alpha(cos \theta + sin \theta) + cos \alpha (cos \theta + sin \theta) }}$

(Sin ∅ + Cos ∅)(Sin @ + Cos @)/ (Sin ∅ + Cos ∅) ( Cos @ - Sin@)

(Sin ∅ + Cos ∅) gets cancelled ! Hence final answer :

${\huge{\bold{\frac{Sin@ + Cos@}{Cos@ - Sin@)}}}}$

Hence Proved❗

${\bold{Identities \:used \:}}$ →:

→ Sin ( A + B ) = SinA.CosB + CosA.SinB

→ Sin ( A - B ) = SinA.CosB - CosA.SinB

→ Cos ( A + B ) = CosA.CosB - SinA.SinB

→ Cos ( A - B ) = CosA.CosB + SinA.SinB

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